Problem 1 Suppose that there were 25 peopl... [FREE SOLUTION]

Chapter 1: Problem 1

Suppose that there were 25 people who had a reservation price of $\$ 500$ and the 26 th person had a reservation price of $\$ 200$. What would the demand curve look like?

Short Answer

Expert verified

The demand curve is a step-like function that decreases from 25 at $500 to 26 at $200.

Step by step solution

Identify Reservation Prices

There are 25 people who have a reservation price of $500, meaning they are willing to pay up to $500 for a good or service. The 26th person has a reservation price of $200, meaning they are willing to pay up to $200.

Construct Demand Schedule

We construct a demand schedule, which is a table that shows the quantity demanded at each price level. For prices above $500, the quantity demanded is 0, as no one is willing to pay that much. At exactly $500, 25 people are willing to buy the product. At exactly $200, 26 people (including the person with the lower reservation price) are willing to buy.

Draw the Demand Curve

The demand curve is drawn by plotting the price against the quantity demanded on the graph. The curve starts at a quantity of 25 at a price of $500 and decreases to 26 at a price of $200, creating a step-wise pattern. For prices between $200 and $500, the quantity demanded is static at 25.

Analyze the Shape

The demand curve will have a horizontal line at $500 from a quantity of 0 to 25, quickly dropping down to 26 at $200, making it step-like. At prices below $200, the curve remains at 26 units demanded.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Reservation Price

The reservation price is a key concept in understanding consumer behavior. It is the maximum price that a consumer is willing to pay for a good or service. In the context of our original exercise, we have two distinct reservation prices: $500 and $200. A buyer with a reservation price of $500 values the product highly, indicating a strong desire or need for it.

The 26th person in our scenario has a reservation price of $200, suggesting they have a lower willingness to pay compared to the first 25 people.

When the market price exceeds a consumer's reservation price, they will opt out of purchasing the item.
This measurement can help sellers understand pricing strategies and target consumers within different price brackets.

A seller's goal is typically to set a price close to or at the reservation price of the majority, maximizing sales volume while maintaining profitability.

Demand Schedule

A demand schedule is a vital tool used to illustrate how quantity demanded varies with price. It is essentially a table or list displaying the quantity of a product that consumers are willing and able to purchase at varying price points.

In our scenario, the demand schedule can be constructed by noting down the price levels and corresponding quantities demanded:

At a price above $500, the quantity demanded is zero, as no consumer agrees to purchase at such a rate.
At a price of exactly $500, 25 individuals are ready to buy.
Reducing the price to $200 allows a total of 26 people to commit to purchasing the product.

The demand schedule helps in visualizing consumer preferences and can guide businesses in price setting and inventory decisions.

Quantity Demanded

Quantity demanded specifies the total amount of goods or services consumers are willing to buy at a given price. It is influenced by several factors, primarily price, as demonstrated in our exercise.

In simple terms, as the price drops from $500 to $200, the quantity demanded increases from 25 to 26. This illustrates the law of demand, which states that, all else being equal, as the price of a good decreases, the quantity demanded increases.

Prices above $500 result in a quantity demanded of zero because buyers find it too expensive.
A specific group of 25 buyers are prepared to purchase at $500, highlighting their reservation price.
Once the price lowers to $200, an additional buyer is willing to enter the market.

Understanding quantity demanded is crucial for businesses as it informs production levels and marketing strategies.